In this book some mathematical and statistical models have been specified for forecasting and proposed certain criteria for choosing an appropriate forecasting model.the general method of forecasting by using regression model with the estimates of the parameters of the general linear statistical model has been described along with the estimates of the parameters of the general linear statistical model has been described along with the properties of the forecasts.Different stationary and non stationary autoregressive and moving averege processes such as AR(1),AR(2),ARMA(p,q) and ARMA(p,d,q) models have been proposed forecasting in this book.A new statistical forecasting errors to obtain good forecasts.A goodness of fit criterion for ARMA model has been suggested by using the variance ratio test statistics.Further a Modified selection criterion for selecting a forecasting model has been proposed in the book,Here,two modified criteria namely Akaike Information criterion and Schwartz Bayesian Criterion have been considered for selecting the best forecasting models.